Question

A cube of edge (L) and coefficient of linear expansion ($\alpha$ ) is heated by $1^{\circ }C$. Its surface area increases by :

• A. $6\alpha L^2$
• B. $8\alpha L^2$
• C. $12\alpha L^2$
• D. $2\alpha L^2$

Answer 1

The correct option is C $12\alpha L^2$

We know, $A_2=A_1(1+\beta dt)$, where dt = change in temperature = 1
So, change in area $=A_2-A_1=A_1\beta =A_{1}2\alpha$
Now $A_1=6L^2$
Putting these values we get,
Change in area $=12\alpha L^2$